How do you prove ABC isosceles?

Step-by-step:

2 | 3x + 1 | -4 = 6

2 | 3x + 1 | = 10

| 3x + 1 | = 5

| 3x + 1 | = ±5

Solve for both: 3x + 1 = -5 AND 3x + 1 = 5

3x + 1 = - 5

3x = - 6

x = -2

3x + 1 = 5

3x = 4

x = 4/3

x = -2, 4/3

Answer:

3

Step-by-step explanation

The total cost and the number of minutes of the plan will be $70 and 300 minutes, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A telephone organization offers two month-to-month designs. Plan An expense of $16 in addition to an extra $0.18 for every moment of the call. Plan B costs $28 in addition to an extra $0.14 for every moment of the call.

Let 'y' be the total amount and 'x' be the number of minutes. Then we have

y = 0.18x + 16         ...1

y = 0.14x + 28        ...2

From equations 1 and 2, then we have

0.18x + 16 = 0.14x + 28

0.18x - 0.14x = 28 - 16

0.04x = 12

x = 12 / 0.04

x = 300

Then the value of the variable 'y' will be given as,

y = 0.18(300) + 16

y = 54 + 16

y = $70

The total cost and the number of minutes of the plan will be $70 and 300 minutes, respectively.

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The equation of a line that passes through [tex](-1,3)[/tex] and has a slope [tex]2[/tex] is [tex]y=2x+5[/tex]

The equation of the line passes through the point is [tex](-1,3)[/tex]

One point and the slope are given, we will use one point form i.e.

[tex]y=mx+c.....(1)[/tex]

The point [tex](-1,3)[/tex] satisfies the equation and the slope is [tex]2[/tex]

Plug in these values in (1)

[tex]3=2(-1)+c\\3=-2+c\\c=3+2\\c=5[/tex]

Plug in the value of slope and c is

The equation becomes [tex]y=2x+5[/tex]

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The value of c for the angle of the triangle will be 7.34.

Congruence and likeness tests in geometry require comparing matching sides and angles of polygons. Each side and angle in one polygon is paired with a side or angle in the second polygon in these tests.

Given that in triangle LMN, m∠L = (6c + 35)°. If the exterior angle to ∠L measures 79°,

The value of angle c will be calculated as,

(6c + 35)° = 79°

Apply the mathematical operations and solve further,

6c = 79 - 35

6c = 44

c = 7.34

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True, Every normal unitary operator u: x! x exists.
False, An if only if it is invertible, a matrix qualifies as unitary.

What is the matrix?

A group of numbers built up in a rectangular array with rows and columns. The elements, or entries, of the matrix, are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.

Here, we have

a. Every unitary operator U:X→X is normal as an operator A is unitary if A*A = AA* = I and an operator is normal if A*A = AA*.

Hence, every unitary operator u: x → x is normal.

b. A unitary matrix is always invertible but an invertible matrix need not be unitary. An invertible matrix A is unitary if A⁻¹ = A*

Hence, it is not true.

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The slope of the passing line through the origin is 112.5°.

The slope of a line is given as a tangent ratio.

In this case we have the angle, so the slope would be given as

      tan(7π/8).

Therefore,

The angle the line makes with the horizontal is given in radians here:

                     7π/8

In this degrees, we can use:

180° = π radians

1 radian = 180°/π

5π/8 radians = 5π/8 × 180° /π

                     =5π/8 × 180°/π

                     =112.5°

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The system of equations for the given situation are 14=b-c ; 35=b+c and the speed of boat is 24.5 miles/hr and speed of current is 10.5 miles/hr.

Given,

Distance covered by boat in upstream in 3 hours = 42 miles

Distance covered by boat in downstream in 2 hours = 70 miles.

Let

speed of boat in still water be 'b'

speed of current of stream be 'c'

we know that distance=speed x time

If the boat is moving upstream, the current (which is 'c' miles per hour) will push against it, reducing the boat's speed by 'c' miles per hour. The boat's resulting speed (as it travels upstream) is 'b-c' miles per hour. If, on the other hand, the boat is travelling downstream, the current will push it faster, increasing the boat's speed by 'c' miles per hour. The boat's downstream speed is 'b+c' miles per hour as a result.

Then the system of equations will be

distance while going upstream ,

distance=speed x time

42=(b-c)(3)

14=b-c....i

distance while going downstream,

70=(b+c)(2)

35=b+c....ii

solving eq. i and eq. ii

14=b-c

35=b+c

------------

49=2b

b=24.5

Substitute in eq. i,

14=24.5-c

c=24.5-14

c=10.5

Thus, the boat's speed is 24.5 miles per hour and the current's speed is 10.5 miles per hour.

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There are 12 even integers are there between 200 and 700 whose digits are all different and come from the set (1, 2, 5, 7, 8, 9}.

What is number of permutation?

Take the number of possibilities for each event and multiply it by itself X times, where X is the total number of events in the sequence, to determine the number of permutations.

For instance, four-digit PINs have 10 possible combinations because each digit can range from 0 to 9.

We see that the last digit of the 3 -digit number must be even to have an even number. Therefore, the last digit must either be 2 or 8.

Case 1 - the last digit is 2. We must have the hundreds digit to be 5 and the tens digit to be any 1 of {1,7,8,9}, thus obtaining 4 numbers total.

Case 2 - the last digit is 8. We now can have 2 or 5 to be the hundreds digit, and any choice still gives us 4 choices for the tens digit. Therefore, we have 2 x 4 = 8 numbers.

Adding up our cases, we have 4 + 8 = 12 numbers.

Hence, there are 12 even integers are there between 200 and 700 whose digits are all different and come from the set (1, 2, 5, 7, 8, 9}.

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Complete question:

how many even integers are there between 200 and 700 whose digits are all different and come from the set (1, 2, 5, 7, 8, 9}.

Answer:

In order to prove that (x+3) is a factor of p(x), Serena must show that p(-3) = 0. This means that if we plug -3 into the polynomial p(x), the resulting value must be 0. Therefore, the correct answer is option D, p(-3)=0.

Step-by-step explanation:

Traffic accidents occur according to a poisson distribution.

The probability mass function of the total number of accidents between 8 a.m. and 11 a.m is

P(Z = z) = (e⁻⁸× 8ᶻ) /z! ; z = 0, 1, 2, ...........

= 0 ; otherwise

Let X be the random variable that denotes the number of traffic accidents occurring between 8 am and 9 am.

X ~ P(5) and P(X) = 5

Let Y be random variable that denotes the number of traffic accidents occurring between 9am and 11 am.

Possion process with rate 3 accidents per hour

Y~ P(3)

Let Z be random variable that denotes the number of traffic accidents occurring between 8a.m. and 11 am.

For 8 a.m. to 11 a.m. ,P(Z = X+Y) = P(Z = 3+5 = 8)

Possion probability mass function for it is

P(x, λ ) =(e⁻λ λˣ)/x!

The p.m. f of the total number of accidents between 8 am and 11 am is

P(Z = z) = (e⁻⁸× 8ᶻ) /z! ; z = 0, 1, 2, ...........

= 0 ; otherwise

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Answer:

37

Step-by-step explanation:

50*26%

50-(50*26%)

Yes, there is a correlation between these measures. The higher the placement exam score, the higher the student's score on their first exam tends to be. For example, students with placement exam scores of 11 and 49 had first exam scores of 27 and 71 respectively, indicating that the higher the placement exam score, the higher the first exam score.

A measure in mathematics is a generalization of the ideas of length, area, and volume. Measures are sometimes referred to as "mass distributions" informally. A measure, in more exact terms, is a function that gives numbers to particular subsets of a given set. This quantity is described as the set's measure.

To measure length or distance, this system employs inches, feet, yards, and miles. Volume or capacity are expressed in fluid ounces, cups, pints, quarts, or gallons. In ounces, pounds, and tons, weight or mass is expressed.

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The factorization of the given expression is -3x(xy+3y-1).

The given expression is -3x²y-3x+9xy².

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

The factorization of the given expression is as follows

-3x²y-3x+9xy²

= -3x(xy-1+3y)

= -3x(xy+3y-1)

Therefore, the factorization of the given expression is -3x(xy+3y-1).

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Answer:

3X-9=(6x6)/4

Step-by-step explanation:

Statistics can promote limitations in perception in all the following ways, except by Option C. Considering alternative perspectives when defining variable relationships.

Option C encourages a holistic approach to analyzing statistics, rather than promoting limitations in perception. It encourages the analyst to consider different perspectives when interpreting the data, thus allowing a more comprehensive understanding.

This open-minded approach is essential in order to form valid conclusions. When taking into account multiple perspectives, the analyst is able to come to a more informed conclusion, rather than relying on a single-perspective interpretation. Option C does not promote limitations in perception, as it encourages a more open-minded approach to interpreting the data.

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The option that has the best insight of how to find the experimental probability of rolling a 3 is option A

A. To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials. Simplify if necessary.

An experimental probability is a probability based on real  or actual experiment, such that the result depends on the accuracy of the record of the occurrences during the experiment.

The result from the experiment is presented as follows;

Number  [tex]{}[/tex]                                Frequency

1  [tex]{}[/tex]                                           4

2  [tex]{}[/tex]                                          6

3  [tex]{}[/tex]                                          5

4  [tex]{}[/tex]                                          7

5  [tex]{}[/tex]                                         3

6  [tex]{}[/tex]                                         5

The probability of an event is the ratio of the number of possible outcome to the number of required outcome.

Therefore: The probability of rolling a three is the ratio of the frequency of an outcome of threes to the sum of the frequency of all the events.

The correct option from which the best details of finding an experimental  probability can be obtained is the option that states that the experimental probability of rolling a three is the ratio of the count of the number of times three occurs to the total number of trials, which is the frequency of rolling a three to the sum of all the frequencies in the experiment.

Mathematically, we get;

The probability of an event E, P(E) = [tex]\frac{Number\, of \, outcomes \, three}{Total \, number \, of \, outcomes}[/tex]

Therefore

[tex]P(3) = \dfrac{Number\, of \, times \, three\, occurs }{Total\, number \, of \, trials} = \dfrac{Freqiuency\ of \ 3s }{Sum\ of \ ther \ frequencies}[/tex]

[tex]P(3) = \dfrac{5}{4+6+5+7+3+5} =\dfrac{1}{6}[/tex]

The correct option is option A

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The given expression is showing an inequality.

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Given that, -7x > -35

The given expression is showing  inequality where -7x is greater than -35

On simplifying, we get,

-7x > -35

7x < 35

x < 5

Therefore, x is less than 5

Hence, The given expression is showing an inequality.

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3 colors are the maximum that can be used.

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

each square of the three-by-three grid is painted so that the whole picture has at least the two lines of symmetry indicated.

each grid square is painted one solid color

Based on the symmetry lines the groups that must be the same color are

{1,3,7,9}

{2,4,6,8}

and {5}

Hence, 3 colors are the maximum that can be used.

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[tex]11.5x+10.9y[/tex] when x is 6 and y is 7

Substitute:

[tex]11.5(x)+10.9(y)[/tex]

[tex]11.5(6)+10.9(7)[/tex]

Solve:

[tex]11.5\times6=69\\10.9\times7=76.3[/tex]

[tex]69+76.3[/tex]

[tex]=\fbox{145.3}[/tex]

The sample size should be 24.

What is the sample size?

The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component.

Here, we have

Given

Margin of error = 300

confidence level = 0.9

standard deviation = 900

Assuming the standard deviation to be of population

ME = Z(0.1/2) × σ/√n

300 = 1.645 × 900/√n

n =  {(1.645 × 900)300}²

n = 24

Hence, the sample size should be 24.

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The answer will be (9)

Step-by-step explanation:

The first step to dividing fractions of 18 divide 2 than (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators.

If Sergio read 18 pages of novel in 2 hours, than he's only reading 9 pages at a time than the next!

Answer:

Step-by-step explanation:

i think it is 74

The width, length and height of the box is 12.247 inch, 24.494 inch, 73.482 inch respectively.

We have given that Alina wants to make a rectangular box whose base is twice as long as it's wide and alina has 300 square inches of velvet.

i.e A = l × w

it s given that l = 2w

∴ A = 2w²

⇒ 300 = 2w²

      w² = 150

       w = 12.247 inch

i.e. l = 2w

     l = 2(12.247)

     l = 24.494 inch

Therefore length of the box is 24.494 inch and width is 12.247 inch.

Now we have to find height of the box.

For the height of rectangle we know the formula

i,e, Height = [tex]\frac{P}{2}[/tex] - w

where P is perimeter

we will first find perimeter of rectangle.

Therefore P = 2(l + w)

                 P = 2(24.494 + 12.247)

                 P = 2(36.741)

                 P = 73.482 inch

Hence the height of the rectangle is 73.482 inch.

Therefore the Eliza's box that Alina make has width 12.247 inch, length 24.494 inch and height 73.482 inch.

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The reason asking why the problem occurred This frequently identifies problems with the organization or places where processes need to be addressed.

The process is remarkably straightforward: whenever an issue arises, you ask "Why?" five times to get to the bottom of it. Then, when a remedy emerges, you put it into action to stop the problem from happening again.

The nice thing about 5 Whys is that it challenges you to move beyond blaming and question why that occurred.

This frequently identifies problems with the organization or places where processes need to be addressed.

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26.3 feet is the radius of the curve if the middle ordinate measures 4.8 feet when using a chord with a length of 42ft.

The radius of the curve is 26.3 feet.

1. Use the equation: 2r = chord length/sin of the angle between the chords.

2. Plug in the chord length Just use the chord length formula as follows: Chord length is equal to 2(r2-d2), where r is the circle's radius and d is the chord's perpendicular distance from its center.(42ft) and the middle ordinate (4.8ft) and solve for r.

3. 2r = 42/sin (4.8/2) = 42/ sin 2.4 = 26.3

4. Round answer to the nearest tenth of a foot (one place after the decimal): 26.3 feet.

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The simple interest rate would be 20%. The result is obtained by using the simple interest formula.

The interest of an amount of money can be counted by the following formula.

I = P₁ - P

I = P × r × t

Where

Jesse now has $65,000 and he deposit it in an account. After 18 years, he wishes the balance will grow into $300,000. Determine the simple interest rate!

First, let's find the interest.

I = P₁ - P

I = $300,000 - $65,000

I = $235,000

The simple interest rate is

I = P × r × t

235,000 = 65,000 × r × 18

r = 235,000 / 1,170,000

r = 0.201

r ≈ 20%

Hence, the simple interest rate he would need to deposit his money is 20%.

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Therefore , the p- value is 0.008 , thus half of population is supporting.

A hypothesis is a proposed explanation for a phenomenon. The scientific method states that a theory cannot be deemed scientific unless it has been put to the test. The majority of scientific ideas are founded on historical findings that are insufficiently explained by current knowledge.

Here,

test statistics Z=

Z = [tex]\frac{p-p'}{\sqrt{p'(1-p')/n} }[/tex]

for

H0 : p= 0.5

And

Ha: p>0.5

Z =(0.585-0.5) / ((0.5)(0.5)/200)

Z=2.4

Since p =x/n=117/200=0.585

Thus

p- value= P(Z>2.4)=1-Ф(2.4)=1-0.992 =0.008

Therefore , the p- value is 0.008 , thus half of population is supporting.

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A car is selected from random sample of 100 cars,

a) The events for which the selected car has 2 doors and 4 doors are mutually exclusive event ;

i.e P(A ∩ B) = 0.

b) The probability that a randomly selected car from this sample had 2 doors or 4 doors is 0.77..

Mutually exclusive event :

A and B are mutually exclusive if they cannot occur at the same time. This means that A and B have no common result and P(A and B) = 0.

We have given a Venn diagram which consists the cars have sunroof , 2 doors and 4 doors.

Firstly we need to understand the Venn diagram properly for determining the required probability values.

From Venn diagram ,

Total number of cars in sample = 100

Cars with sunroof only = 13

Number of cars with 2 doors only = 14

Number of cars with 4 doors only = 25

Number of cars with sunroof and 2 doors = 18

Number of cars with sunroof and 4 doors = 20

a) let us consider two events A and B

A : car with two doors

B : car with four doors

As we see in Venn diagram,

the number of cars with 4 doors and 2 door, n(A∩B) = 0 => P(A and B) = 0

so, by definition of mutually exclusive event

A and B are are mutually exclusive events.

b) Probability that car with 2 doors, P(A)

= favourable outcomes for A / total outcomes

= 14+18/100 = 32/100

Probability that car with 4 doors, P(B)

= favourable cases for B/ total outcomes

= 25+20/100 = 45/100

Probability that randomly selected car from this sample had 2 doors or 4 doors = P( A or B)

= P(A) + P(B) = 77/100 = 0.77

Hence, the required probability is 0.77..

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Complete question:

Two-way tables, Venn diagrams, and probability Sunroof 13 10 18 20 14 25 2 doors 4 doors In this sample, are the events "2 doors" and "4 doors" mutually exclusive? Choose 1 answer A Yes O No Find the probability that a randomly selected car from this sample had 2 doors or 4 doors. O of 4